A queue can be implemented using two stacks. Let queue to be implemented be q and stacks used to implement q be stack1 and stack2. q can be implemented in two ways:

Method 1 (By making enQueue operation costly)
This method makes sure that newly entered element is always at the top of stack 1, so that deQueue operation just pops from stack1. To put the element at top of stack1, stack2 is used.

enQueue(q, x)
  1) While stack1 is not empty, push everything from satck1 to stack2.
  2) Push x to stack1 (assuming size of stacks is unlimited).
  3) Push everything back to stack1.

dnQueue(q)
  1) If stack1 is empty then error
  2) Pop an item from stack1 and return it

Method 2 (By making deQueue operation costly)
In this method, in en-queue operation, the new element is entered at the top of stack1. In de-queue operation, if stack2 is empty then all the elements are moved to stack2 and finally top of stack2 is returned.

enQueue(q,  x)
  1) Push x to stack1 (assuming size of stacks is unlimited).

deQueue(q)
  1) If both stacks are empty then error.
  2) If stack2 is empty
       While stack1 is not empty, push everything from satck1 to stack2.
  3) Pop the element from stack2 and return it.

Method 2 is definitely better than method 1. Method 1 moves all the elements twice in enQueue operation, while method 2 (in deQueue operation) moves the elements once and moves elements only if stack2 empty.

Implementation of method 2:

/* Program to implement a queue using two stacks */
#include<stdio.h>
#include<stdlib.h>

/* structure of a stack node */
struct sNode
{
   int data;
   struct sNode *next;
};
 
/* Function to push an item to stack*/
void push(struct sNode** top_ref, int new_data);
 
/* Function to pop an item from stack*/
int pop(struct sNode** top_ref);
 
/* structure of queue having two stacks */
struct queue
{
   struct sNode *stack1;
   struct sNode *stack2;
};
 
/* Function to enqueue an item to queue */
void enQueue(struct queue *q, int x)
{
   push(&q->stack1, x);
}
 
/* Function to dequeue an item from queue */
int deQueue(struct queue *q)
{
   int x; 
 
   /* If both stacks are empty then error */
   if(q->stack1 == NULL && q->stack2 == NULL)
   {
      printf("Q is empty");
      getchar();
      exit(0);
   }

   /* Move elements from satck1 to stack 2 only if 
       stack2 is empty */
   if(q->stack2 == NULL)
   {
     while(q->stack1 != NULL)
     {
        x = pop(&q->stack1);
        push(&q->stack2, x);
     }
   } 

   x = pop(&q->stack2);
   return x;
}
 
/* Function to push an item to stack*/
void push(struct sNode** top_ref, int new_data)
{
  /* allocate node */
  struct sNode* new_node =
            (struct sNode*) malloc(sizeof(struct sNode));
 
  if(new_node == NULL)
  {
     printf("Stack overflow \n");
     getchar();
     exit(0);
  }            
 
  /* put in the data  */
  new_node->data  = new_data;
 
  /* link the old list off the new node */
  new_node->next = (*top_ref);   
 
  /* move the head to point to the new node */
  (*top_ref)    = new_node;
}
 
/* Function to pop an item from stack*/
int pop(struct sNode** top_ref)
{
  int res;
  struct sNode *top;
 
  /*If stack is empty then error */
  if(*top_ref == NULL)
  {
     printf("Stack overflow \n");
     getchar();
     exit(0);
  }
  else
  {
     top = *top_ref;
     res = top->data;
     *top_ref = top->next;
     free(top);
     return res;
  }
}
 
/* Driver function to test anove functions */
int main()
{
   /* Create a queue with items 1 2 3*/
   struct queue *q = (struct queue*)malloc(sizeof(struct queue));
   q->stack1 = NULL;
   q->stack2 = NULL;
   enQueue(q, 1);
   enQueue(q, 2);
   enQueue(q, 3);    
 
   /* Dequeue items */
   printf("%d  ", deQueue(q));
   printf("%d  ", deQueue(q));
   printf("%d  ", deQueue(q));  
 
   getchar();
}

Queue can also be implemented using one user stack and one Function Call Stack.
Below is modified Method 2 where recursion (or Function Call Stack) is used to implement queue using only one user defined stack.

enQueue(x)
  1) Push x to stack1.

deQueue:
  1) If stack1 is empty then error.
  2) If stack1 has only one element then return it.
  3) Recursively pop everything from the stack1, store the popped item 
    in a variable res,  push the res back to stack1 and return res

The step 3 makes sure that the last popped item is always returned and since the recursion stops when there is only one item in stack1 (step 2), we get the last element of stack1 in dequeue() and all other items are pushed back in step 3.

Implementation of method 2 using Function Call Stack:

/* Program to implement a queue using one user defined stack and one Function Call Stack */
#include<stdio.h>
#include<stdlib.h>
 
/* structure of a stack node */
struct sNode
{
   int data;
   struct sNode *next;
};
 
/* structure of queue having two stacks */
struct queue
{
  struct sNode *stack1;
};
 
/* Function to push an item to stack*/
void push(struct sNode** top_ref, int new_data);
 
/* Function to pop an item from stack*/
int pop(struct sNode** top_ref);
 
/* Function to enqueue an item to queue */
void enQueue(struct queue *q, int x)
{
  push(&q->stack1, x);
}
 
/* Function to dequeue an item from queue */
int deQueue(struct queue *q)
{
   int x, res; 
 
   /* If both stacks are empty then error */
   if(q->stack1 == NULL)
   {
     printf("Q is empty");
     getchar();
     exit(0);
   }
   else if(q->stack1->next == NULL)
   {
      return pop(&q->stack1);
   }
   else
   {
      /* pop an item from the stack1 */
      x = pop(&q->stack1);
 
      /* store the last dequeued item */
      res = deQueue(q);
 
      /* push everything back to stack1 */
      push(&q->stack1, x);
 
      return res;
   }
}
 
/* Function to push an item to stack*/
void push(struct sNode** top_ref, int new_data)
{
  /* allocate node */
  struct sNode* new_node =
            (struct sNode*) malloc(sizeof(struct sNode));
 
  if(new_node == NULL)
  {
     printf("Stack overflow \n");
     getchar();
     exit(0);
  }           
 
  /* put in the data  */
  new_node->data  = new_data;
 
  /* link the old list off the new node */
  new_node->next = (*top_ref);  
 
  /* move the head to point to the new node */
  (*top_ref)    = new_node;
}
 
/* Function to pop an item from stack*/
int pop(struct sNode** top_ref)
{
  int res;
  struct sNode *top;
 
  /*If stack is empty then error */
  if(*top_ref == NULL)
  {
     printf("Stack overflow \n");
     getchar();
     exit(0);
  }
  else
  {
     top = *top_ref;
     res = top->data;
     *top_ref = top->next;
     free(top);
     return res;
  }
} 
 
/* Driver function to test above functions */
int main()
{
  /* Create a queue with items 1 2 3*/
  struct queue *q = (struct queue*)malloc(sizeof(struct queue));
  q->stack1 = NULL;
 
  enQueue(q, 1);
  enQueue(q, 2);
  enQueue(q, 3);    
 
  /* Dequeue items */
  printf("%d  ", deQueue(q));
  printf("%d  ", deQueue(q));
  printf("%d  ", deQueue(q));  
 
  getchar();
}



Please write comments if you find any of the above codes/algorithms incorrect, or find better ways to solve the same problem.

         

Related Tpoics: